Mount requires surgery on a problematic pelvic while James is sidelined with a hamstring injury.
James has endured a frustrating time with injuries this season and missed the FIFA World Cup in Qatar last year due to a knee problem.
The England right back made only 24 appearances for Chelsea this season across all competitions, scoring two goals and providing two assists.
Mount has not had the best of seasons despite making 35 appearances in all competitions. He only has three goals and four assists for the campaign.
Speaking ahead of Tuesday's home game against Brentford, Chelsea's interim manager Frank Lampard said: “Reece James is unavailable, probably out for the season. Mason is probably the same. There’s potential for him to be back for the last game of the season but probably not.
“That’s obviously disappointing for us. Kai [Havertz] is struggling a little bit with his knee so won’t be available tomorrow but the good news is that he should be available by the end of the week.
“It is a blow for all of us as they’re all big players. Reece had a hamstring injury that he picked up against Madrid. He got it in the game and we picked it up with scans in the following few days.
“Mason has been carrying this pelvic injury for a while and it pre-dates myself for a while. I have been trying and the medical staff have been trying.
“But it has got to the stage where he will have a minor surgery and it will probably be a four-week recovery.”
Chelsea, eleventh on the table, are without a win in five Premier League games.
